linux kernel page table synchronization

linux kernel page table synchronization

In linux x86 paging.
1. each process has it's own page directory.
2. page table walking starts with page directory which is pointed by CR3.
3. every process shares the kernel page directory content
assuming three sentences are correct, let's say some process enters kernel
mode and updates his kernel page directory content(address mapping, access
rights, etc...)
Question. since kernel address spaces is globally shared among processes,
this update has to be synchronized with other process's page directory,
right?
how can this be managed?
thank you in advance.